Question

The object at rest suddenly explodes into three parts with the mass ratio $2:1:1$. The parts of equal mass move at right angles to each other with equal speeds. The speed of the third part after the explosion will be :

• A. $2V$
• B. $\frac{V}{\sqrt{2}}$
• C. $\frac{V}{2}$
• D. $\sqrt{2}V$

Answer 1

Answer: (B)

$\frac{V}{\sqrt{2}}$

Using momentum conservation,

$0=(\frac{m}{2}\times V_y+\frac{m}{4}\times V).\hat{j}+(\frac{m}{4}\times V+\frac{m}{2}\times V_x).\hat{i}$

$\Rightarrow V_y=-\frac{V}{2}\hat{j}$

$V_x=-\frac{V}{2}\hat{i}$

$\left|\overrightarrow{V}\right|=\sqrt{V_y^2+V_x^2}$

$=\frac{V}{\sqrt{2}}$